The Vavilov–Cerenkov effect and the Doppler effect in the motion of sources with superluminal velocity in vacuum

It is customary to consider only “subluminal” light sources, or sources moving with a velocity $v$ lower than the velocity of light in vacuum $(c)$. It is assumed in this connection that the Vavilov–Cerenkov effect and the anomalous Doppler effect are possible only in media and waves for which the refractive index $n(\omega)>1$. For this reason, the phase velocity of the waves is $c_{ph}=[c/n(\omega)]<c$, and these waves can be emitted by a subluminal source if $v>c_{ph}$. Yet, as is well known, there exist also “superluminal” sources, with velocity $v>c$. Examples are light spots produced on a remote screen by a rotating source of light or particles. The spot velocity is $v=\Omega R$, where $\Omega$ is the angular velocity of source rotation and $R$ is the distance to the screen. The condition $v>c$ can be realized on the Earth, and is practically always realized under astronomical conditions for pulsar radiation. It is emphasized in the article that superluminal sources are equivalent in a wide range to subluminal ones, and, concretely, can generate Cerenkov radiation in vacuum and in a medium with $n(\omega)<1$. The article considers several corresponding possibilities. From this point of view of radiation theory, a major difference between the superluminal and subluminal sources is that the former can not be individual particles (electrons, protons, etc.), since their velocity is always smaller than $c$. Superluminal sources, which must thus consist of aggregates of particles, must thus have nonzero dimensions, and this leads to a corresponding formation of a spectrum of the radiated frequencies on the short-wave side. Regardless of whether superluminal sources will find interesting applications in physics and astronomy, a study of the radiation of superluminal sources of electromagnetic and gravitational waves (and possibly also neutrinos) is in the authors' opinion of undisputed physical interest.